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Abstract

Background: The estimation of parameter values continues to be the bottleneck of the
computational analysis of biological systems. It is therefore necessary to develop improved
methods that are effective, fast, and scalable.
Results: We show here that alternating regression (AR), applied to S-system models and combined
with methods for decoupling systems of differential equations, provides a fast new tool for
identifying parameter values from time series data. The key feature of AR is that it dissects the
nonlinear inverse problem of estimating parameter values into iterative steps of linear regression.
We show with several artificial examples that the method works well in many cases. In cases of no
convergence, it is feasible to dedicate some computational effort to identifying suitable start values
and search settings, because the method is fast in comparison to conventional methods that the
search for suitable initial values is easily recouped. Because parameter estimation and the
identification of system structure are closely related in S-system modeling, the AR method is
beneficial for the latter as well. Specifically, we show with an example from the literature that AR
is three to five orders of magnitudes faster than direct structure identifications in systems of
nonlinear differential equations.
Conclusion: Alternating regression provides a strategy for the estimation of parameter values and
the identification of structure and regulation in S-systems that is genuinely different from all existing
methods. Alternating regression is usually very fast, but its convergence patterns are complex and
will require further investigation. In cases where convergence is an issue, the enormous speed of
the method renders it feasible to select several initial guesses and search settings as an effective
countermeasure.